The man can row the boat in still water with a speed of
5 m> s. If the river is flowing at 2 m> s, determine the speed
of the boat and the angle u he must direct the boat so that it
travels from A to B.
The airplane is traveling in a straight line with a speed of
300 km> h, when the engines A and B produce a thrust of
TA = 40 kN and TB = 20 kN, respectively. Determine the
angular velocity of the airplane in t = 5 s. The plane has a
mass of 200 Mg, i
The 30-kg uniform slender rod AB rests in the position
shown when the couple moment of M = 150 N # m is
applied. Determine the initial angular acceleration of the
rod. Neglect the mass of the rollers.
Equations of Motion: Here, th
The cable is subjected to a force of P = 20 lb, and the spool
rolls up the rail without slipping. Determine the angular
velocity of the spool in 5 s, starting from rest. The spool has
a weight of 100 lb and a radius of gyration about its center
The similar links AB and CD rotate about the fixed pins at
A and C. If AB has an angular velocity vAB = 8 rad> s,
determine the angular velocity of BDP and the velocity of
AB = 8 rad/s
A passenger in an automobile observes that raindrops make
an angle of 30 with the horizontal as the auto travels
forward with a speed of 60 km/h. Compute the terminal
(constant)velocity vr of the rain if it is assumed to fall
va = 60
The 20-lb box slides on the surface for which mk = 0.3. The
box has a velocity v = 15 ft> s when it is 2 ft from the plate.
If it strikes the smooth plate, which has a weight of 10 lb and
is held in position by an unstretched spring of stiffness
The 30-kg gear A has a radius of gyration about its center of
mass O of kO = 125 mm. If the 20-kg gear rack B is
subjected to a force of P = 200 N, determine the time
required for the gear to obtain an angular velocity of
20 rad>s, starting from res
The acceleration of a particle traveling along a straight line
is a = s m>s2, where s is in meters. If v = 0, s = 1 m
when t = 0, determine the particles velocity at s = 2 m.
v dv = a ds
v dv =
When the motorcyclist is at A, he increases his speed along
the vertical circular path at the rate of v = (0.04s) ft>s2
where s is in ft. If he starts at vA = 2 ft>s where s = 0 at A,
determine the magnitude of his velocity when he reaches B.
The 30-kg reel is mounted on the 20-kg cart. If the cable
wrapped around the inner hub of the reel is subjected to a
force of P = 50 N, determine the velocity of the cart and
the angular velocity of the reel when t = 4 s. The radius of
gyration of t
Tests reveal that a normal driver takes about 0.75 s before
he or she can react to a situation to avoid a collision. It takes
about 3 s for a driver having 0.1% alcohol in his system to
do the same. If such drivers are traveling on a straight road
A car is to be hoisted by elevator to the fourth floor of a
parking garage, which is 48 ft above the ground. If the
elevator can accelerate at 0.6 ft> s2, decelerate at 0.3 ft> s2,
and reach a maximum speed of 8 ft> s, determine the
shortest time to
At t = 0 bullet A is fired vertically with an initial (muzzle)
velocity of 450 m/s. When t = 3 s, bullet B is fired upward
with a muzzle velocity of 600 m/s. Determine the time t, after
A is fired, as to when bullet B passes bullet A. At what
A particle is moving along a straight line such that when it
is at the origin it has a velocity of 4 m> s. If it begins to
decelerate at the rate of a = 1 - 1.5v1>22 m> s2, where v is in
m> s, determine the distance it travels before it stops.
The acceleration of a particle along a straight line is defined
by a = 12t - 92 m> s2, where t is in seconds. At t = 0,
s = 1 m and v = 10 m> s. When t = 9 s, determine (a) the
particles position, (b) the total distance traveled, and
(c) the velocit
A particle is moving along a straight line such that its
velocity is defined as v = ( - 4s2) m> s, where s is in meters.
If s = 2 m when t = 0, determine the velocity and
acceleration as functions of time.
v = - 4s2
= - 4s2
When the bicycle passes point A, it has a speed of 6 m> s,
which is increasing at the rate of v = 10.52 m> s2. Determine
the magnitude of its acceleration when it is at point A.
12 ln (
Radius of Curvature:
y = 12 ln
At a given instant the train engine at E has a speed of
20 m> s and an acceleration of 14 m> s2 acting in the
direction shown. Determine the rate of increase in the
trains speed and the radius of curvature r of the path.
at = 14 c
From a videotape, it was observed that a pro football player
kicked a football 126 ft during a measured time of
3.6 seconds. Determine the initial speed of the ball and the
angle u at which it was kicked.
s = s0 + v0 t
A golf ball is struck with a velocity of 80 ft> s as shown.
Determine the distance d to where it will land.
Horizontal Motion: The horizontal component of velocity is (v0)x = 80 cos 55
= 45.89 ft> s.The initial and f
Pin P is constrained to move along the curve defined by the
lemniscate r = (4 sin 2u) ft. If the slotted arm OA rotates
counterclockwise with a constant angular velocity of
u = 1.5 rad> s, determine the magnitudes of the velocity and
The man pulls the boy up to the tree limb C by walking
backward at a constant speed of 1.5 m> s. Determine the
speed at which the boy is being lifted at the instant
xA = 4 m. Neglect the size of the limb. When xA = 0,
yB = 8 m, so that A and B are
Cars A and B are traveling around the circular race track.
At the instant shown, A has a speed of 90 ft> s and is
increasing its speed at the rate of 15 ft> s2, whereas B has a
speed of 105 ft> s and is decreasing its speed at 25 ft> s2.
Determine the displacement of the log if the truck at C
pulls the cable 4 ft to the right.
2sB + (sB - sC) = l
3sB - sC = l
3 sB - sC = 0
Since sC = - 4, then
3 sB = - 4
sB = - 1.33 ft = 1.33 ft :
When u = 15, the car has a speed of 50 m> s which is
increasing at 6 m> s2. Determine the angular velocity of the
camera tracking the car at this instant.
(100 cos 2u) m
r = 100 cos 2u
r = ( - 200 (sin 2u) u ) m>
The block B, having a mass of 0.2 kg, is attached to the
vertex A of the right circular cone using a light cord. If the
block has a speed of 0.5 m>s around the cone, determine
the tension in the cord and the reaction which the cone
exerts on the b
The car travels along the circular curve having a radius
r = # 400 ft. At the instant shown, its angular rate of rotation
is u = 0.025 rad> s, which is decreasing at the rate
u = - 0.008 rad> s2. Determine the radial and transverse
The boy of mass 40 kg is sliding down the spiral slide at a
constant speed such that his position, measured from the
top of the chute, has components r = 1.5 m, u = 10.7t2 rad,
and z = 1 - 0.5t2 m, where t is in seconds. Determine the